“Appointing a new member of the U.S. Senate is a solemn duty, and I take this responsibility with utmost seriousness,” Haley said in a statement. “I will make this decision in a manner that is thoughtful and dignified, but also quickly.”

The first-term governor knocked down the possibility that she might appoint herself and said she would appoint a conservative.

“I want to make two things clear from the outset. Number one, I will not take the appointment myself. Number two, I will appoint a person who has the same philosophy of government that Jim DeMint and I share,” she said. “With all the challenges we face as a state and nation, it is essential that the next senator from South Carolina be dedicated to the principles that our state most values.”

Among the top GOP names floated for a potential Haley appointment: freshman Rep. Tim Scott, former state Attorney General Henry McMaster and state Rep. Nathan Ballentine.

The appointed senator will serve through the 113th Congress but will face voters in 2014 to fill out the remainder of DeMint’s term, which runs through 2016. DeMint announced Thursday that he would resign in January.